It’s not exactly news that fruits and veggies are good for you. But historically, physicians have been reluctant to make any diet recommendations at all to their patients. Medical schools don’t teach much about nutrition.

Andrew Freeman, a cardiologist with National Jewish Health hospital in Denver, Colorado, says that doctors often worry that patients will balk at the idea of radically altering what they eat. But that’s slowly changing: Freeman, who follows a vegan diet himself, now recommends a “plant-based diet” to his patients...